Elizabeth Anscombe, answered from the texts and cited to the page.
"I" is not a referring expression. There is no Cartesian self — no inner mental object, no soul-substance, no transcendental subject — picked out by the first-person pronoun.1 The Cartesian temptation to posit such a referent arises from a grammatical illusion: from treating "I" as if it functioned like a proper name or a demonstrative ("this person here") whose semantic contribution is to pick out a particular individual.23
Linguistic analysis of how "I" actually functions in self-reference, indexical reports, and self-ascription shows that the referential model breaks down. What "I" does — the work it does in language and in self-knowledge — is not the work of singular reference. The thesis is Wittgensteinian in method (the Investigations on the Cartesian inner, the Tractatus on the philosophical "I") and Aristotelian in framework (the unity of the human being is psychophysical, not ego-substantial).4
With that thought: "The J was subject, not object, and hence invisible'', we have an example of language itself being as it were possessed of an imagination, forcing its image upon us. The dispute is self-perpetuating, endless, irresoluble, so long as we adhere to the initial assumption, made so far by all the parties to it: that "I" is a referring expression.VOLUME TWO, p. 32
Nevertheless, these are embarrassing credentials for such inquiries. And a self can be thought of as what "I'"' stands for, or indicates, without taking "I" as a proper name. The reasons for considering it as a proper name were two: first, that to the logician's eye it is one, and second, that it seemed to be just like our ""A"' (which was clearly a proper name) except that it expressed 'self-consciousness'.VOLUME TWO, p. 27
To say all this is to treat "I'' as a sort of proper name. That's what gets us into this jam. Certainly "'I"' functions syntactically like a name. However, it has been observed not to be a proper name. Now this observation may strike us as obvious enough in a trivial sense. After all, we don't call it a proper noun but a personal pronoun. It is at any rate not an ordinary proper name.VOLUME TWO, pp. 23–24
How do I know that 'I' is not ten thinkers thinking in unison? Or perhaps not quite succeeding. That might account for the confusion of thought which I sometimes feel. — Consider the reply 'Legion, for we are many'', given by the possessed man in the gospel. Perhaps we should take that solemnly, not as a grammatical joke.® These considerations refute the 'definite description' account of ""I''.VOLUME TWO, p. 32
The First Person (1975) is the most contested single thesis in her philosophy of mind. Strawson, Castaneda, and the wider analytic tradition treat "I" as a referring expression, however subtle; O'Brien, Rödl, and the Wittgensteinian-Aristotelian tradition defend something close to the Anscombian thesis. Kripke's Naming and Necessity is the broader background within which the contemporary debate over indexical reference takes shape. The thesis is contested for the right reasons — it dissolves a picture deep in the philosophical tradition — and it remains a live position rather than a footnote.